Influence of Equation Nonlinearity on Pulse-Decay Permeability Measurements of Tight Porous Media

The pulse-decay method is believed to be more suitable than the steady-state method for permeability measurements on tight porous media because it records pressure variations instead of flow rates and does not require the establishment of a steady state. Most of the previous analytical solutions for the pulse-decay process are based on a linearized governing equation, which may be inapplicable to measurements with large differential pressures. In this study, a nonlinear governing equation is derived through mass conservation and Darcy's law. For rigid porous media such as the sedimentary rock samples, by comparing the magnitude of the pressure sensitivity of the physical properties for both the testing gas and the core sample, we found that only the gas compressibility and the apparent permeability have to be regarded as pressure-dependent, while the others can be regarded as constant. The perturbation method and the eigenfunction expansion method are combined to derive the general solution of the nonlinear governing equation. The results show that in the plot of logarithmic differential pressure versus time, a straight line can be obtained at the late-time stage and its slope value can be used to evaluate the apparent permeability. We further estimate the error in permeability evaluation, induced by selecting mean pore pressure as the characteristic pressure. The theoretical analysis has been verified by both numerical simulation and experimental measurements.